LMFDB - Embedded newform 8021.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13613 q^{2} -0.639809 q^{3} +2.56307 q^{4} +0.116719 q^{5} +1.36672 q^{6} -4.16794 q^{7} -1.20279 q^{8} -2.59064 q^{9} +O(q^{10})$	\(q-2.13613 q^{2} -0.639809 q^{3} +2.56307 q^{4} +0.116719 q^{5} +1.36672 q^{6} -4.16794 q^{7} -1.20279 q^{8} -2.59064 q^{9} -0.249327 q^{10} -2.18943 q^{11} -1.63987 q^{12} +1.00000 q^{13} +8.90327 q^{14} -0.0746777 q^{15} -2.55682 q^{16} -5.42435 q^{17} +5.53396 q^{18} -4.50627 q^{19} +0.299158 q^{20} +2.66669 q^{21} +4.67691 q^{22} +0.268865 q^{23} +0.769553 q^{24} -4.98638 q^{25} -2.13613 q^{26} +3.57695 q^{27} -10.6827 q^{28} +0.610255 q^{29} +0.159522 q^{30} +3.63934 q^{31} +7.86729 q^{32} +1.40082 q^{33} +11.5871 q^{34} -0.486476 q^{35} -6.63999 q^{36} +4.94383 q^{37} +9.62600 q^{38} -0.639809 q^{39} -0.140388 q^{40} +8.74980 q^{41} -5.69640 q^{42} +5.96416 q^{43} -5.61165 q^{44} -0.302377 q^{45} -0.574332 q^{46} -10.1139 q^{47} +1.63588 q^{48} +10.3717 q^{49} +10.6516 q^{50} +3.47055 q^{51} +2.56307 q^{52} +9.56348 q^{53} -7.64084 q^{54} -0.255547 q^{55} +5.01314 q^{56} +2.88316 q^{57} -1.30359 q^{58} +1.41872 q^{59} -0.191404 q^{60} +2.18256 q^{61} -7.77411 q^{62} +10.7976 q^{63} -11.6919 q^{64} +0.116719 q^{65} -2.99233 q^{66} +10.5917 q^{67} -13.9030 q^{68} -0.172022 q^{69} +1.03918 q^{70} +4.72003 q^{71} +3.11599 q^{72} +0.843058 q^{73} -10.5607 q^{74} +3.19033 q^{75} -11.5499 q^{76} +9.12541 q^{77} +1.36672 q^{78} -1.95170 q^{79} -0.298429 q^{80} +5.48337 q^{81} -18.6907 q^{82} -11.1761 q^{83} +6.83490 q^{84} -0.633123 q^{85} -12.7402 q^{86} -0.390447 q^{87} +2.63341 q^{88} +3.22727 q^{89} +0.645917 q^{90} -4.16794 q^{91} +0.689119 q^{92} -2.32848 q^{93} +21.6046 q^{94} -0.525967 q^{95} -5.03356 q^{96} +7.57684 q^{97} -22.1554 q^{98} +5.67203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.13613	−1.51047	−0.755237	−	0.655452i	$-0.772478\pi$
$2$	−2.13613	−1.51047	−0.755237	+	0.655452i	$0.772478\pi$
$3$	−0.639809	−0.369394	−0.184697	−	0.982795i	$-0.559130\pi$
$3$	−0.639809	−0.369394	−0.184697	+	0.982795i	$0.559130\pi$
$4$	2.56307	1.28153
$5$	0.116719	0.0521982	0.0260991	−	0.999659i	$-0.491691\pi$
$5$	0.116719	0.0521982	0.0260991	+	0.999659i	$0.491691\pi$
$6$	1.36672	0.557960
$7$	−4.16794	−1.57533	−0.787666	−	0.616102i	$-0.788711\pi$
$7$	−4.16794	−1.57533	−0.787666	+	0.616102i	$0.788711\pi$
$8$	−1.20279	−0.425249
$9$	−2.59064	−0.863548
$10$	−0.249327	−0.0788440
$11$	−2.18943	−0.660138	−0.330069	−	0.943957i	$-0.607072\pi$
$11$	−2.18943	−0.660138	−0.330069	+	0.943957i	$0.607072\pi$
$12$	−1.63987	−0.473391
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.90327	2.37950
$15$	−0.0746777	−0.0192817
$16$	−2.55682	−0.639206
$17$	−5.42435	−1.31560	−0.657799	−	0.753194i	$-0.728512\pi$
$17$	−5.42435	−1.31560	−0.657799	+	0.753194i	$0.728512\pi$
$18$	5.53396	1.30437
$19$	−4.50627	−1.03381	−0.516905	−	0.856043i	$-0.672916\pi$
$19$	−4.50627	−1.03381	−0.516905	+	0.856043i	$0.672916\pi$
$20$	0.299158	0.0668937
$21$	2.66669	0.581919
$22$	4.67691	0.997121
$23$	0.268865	0.0560622	0.0280311	−	0.999607i	$-0.491076\pi$
$23$	0.268865	0.0560622	0.0280311	+	0.999607i	$0.491076\pi$
$24$	0.769553	0.157084
$25$	−4.98638	−0.997275
$26$	−2.13613	−0.418930
$27$	3.57695	0.688384
$28$	−10.6827	−2.01884
$29$	0.610255	0.113322	0.0566608	−	0.998393i	$-0.481955\pi$
$29$	0.610255	0.113322	0.0566608	+	0.998393i	$0.481955\pi$
$30$	0.159522	0.0291245
$31$	3.63934	0.653644	0.326822	−	0.945086i	$-0.394022\pi$
$31$	3.63934	0.653644	0.326822	+	0.945086i	$0.394022\pi$
$32$	7.86729	1.39075
$33$	1.40082	0.243851
$34$	11.5871	1.98718
$35$	−0.486476	−0.0822295
$36$	−6.63999	−1.10667
$37$	4.94383	0.812761	0.406381	−	0.913704i	$-0.366791\pi$
$37$	4.94383	0.812761	0.406381	+	0.913704i	$0.366791\pi$
$38$	9.62600	1.56154
$39$	−0.639809	−0.102452
$40$	−0.140388	−0.0221972
$41$	8.74980	1.36649	0.683244	−	0.730190i	$-0.260568\pi$
$41$	8.74980	1.36649	0.683244	+	0.730190i	$0.260568\pi$
$42$	−5.69640	−0.878974
$43$	5.96416	0.909526	0.454763	−	0.890613i	$-0.349724\pi$
$43$	5.96416	0.909526	0.454763	+	0.890613i	$0.349724\pi$
$44$	−5.61165	−0.845989
$45$	−0.302377	−0.0450756
$46$	−0.574332	−0.0846806
$47$	−10.1139	−1.47526	−0.737631	−	0.675204i	$-0.764055\pi$
$47$	−10.1139	−1.47526	−0.737631	+	0.675204i	$0.764055\pi$
$48$	1.63588	0.236119
$49$	10.3717	1.48167
$50$	10.6516	1.50636
$51$	3.47055	0.485974
$52$	2.56307	0.355433
$53$	9.56348	1.31364	0.656822	−	0.754046i	$-0.271900\pi$
$53$	9.56348	1.31364	0.656822	+	0.754046i	$0.271900\pi$
$54$	−7.64084	−1.03979
$55$	−0.255547	−0.0344580
$56$	5.01314	0.669908
$57$	2.88316	0.381884
$58$	−1.30359	−0.171169
$59$	1.41872	0.184702	0.0923510	−	0.995727i	$-0.470562\pi$
$59$	1.41872	0.184702	0.0923510	+	0.995727i	$0.470562\pi$
$60$	−0.191404	−0.0247102
$61$	2.18256	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$61$	2.18256	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$62$	−7.77411	−0.987313
$63$	10.7976	1.36038
$64$	−11.6919	−1.46149
$65$	0.116719	0.0144772
$66$	−2.99233	−0.368331
$67$	10.5917	1.29398	0.646988	−	0.762500i	$-0.276028\pi$
$67$	10.5917	1.29398	0.646988	+	0.762500i	$0.276028\pi$
$68$	−13.9030	−1.68598
$69$	−0.172022	−0.0207091
$70$	1.03918	0.124206
$71$	4.72003	0.560164	0.280082	−	0.959976i	$-0.409638\pi$
$71$	4.72003	0.560164	0.280082	+	0.959976i	$0.409638\pi$
$72$	3.11599	0.367223
$73$	0.843058	0.0986725	0.0493362	−	0.998782i	$-0.484289\pi$
$73$	0.843058	0.0986725	0.0493362	+	0.998782i	$0.484289\pi$
$74$	−10.5607	−1.22766
$75$	3.19033	0.368388
$76$	−11.5499	−1.32486
$77$	9.12541	1.03994
$78$	1.36672	0.154750
$79$	−1.95170	−0.219583	−0.109792	−	0.993955i	$-0.535018\pi$
$79$	−1.95170	−0.219583	−0.109792	+	0.993955i	$0.535018\pi$
$80$	−0.298429	−0.0333654
$81$	5.48337	0.609263
$82$	−18.6907	−2.06405
$83$	−11.1761	−1.22673	−0.613366	−	0.789799i	$-0.710185\pi$
$83$	−11.1761	−1.22673	−0.613366	+	0.789799i	$0.710185\pi$
$84$	6.83490	0.745748
$85$	−0.633123	−0.0686718
$86$	−12.7402	−1.37382
$87$	−0.390447	−0.0418603
$88$	2.63341	0.280723
$89$	3.22727	0.342090	0.171045	−	0.985263i	$-0.445286\pi$
$89$	3.22727	0.342090	0.171045	+	0.985263i	$0.445286\pi$
$90$	0.645917	0.0680856
$91$	−4.16794	−0.436919
$92$	0.689119	0.0718456
$93$	−2.32848	−0.241452
$94$	21.6046	2.22834
$95$	−0.525967	−0.0539630
$96$	−5.03356	−0.513736
$97$	7.57684	0.769311	0.384656	−	0.923060i	$-0.374320\pi$
$97$	7.57684	0.769311	0.384656	+	0.923060i	$0.374320\pi$
$98$	−22.1554	−2.23803
$99$	5.67203	0.570061
$100$	−12.7804	−1.27804
$101$	9.84619	0.979733	0.489866	−	0.871798i	$-0.337046\pi$
$101$	9.84619	0.979733	0.489866	+	0.871798i	$0.337046\pi$
$102$	−7.41355	−0.734051
$103$	6.82986	0.672966	0.336483	−	0.941690i	$-0.390763\pi$
$103$	6.82986	0.672966	0.336483	+	0.941690i	$0.390763\pi$
$104$	−1.20279	−0.117943
$105$	0.311252	0.0303751
$106$	−20.4289	−1.98423
$107$	−15.6351	−1.51150	−0.755750	−	0.654860i	$-0.772728\pi$
$107$	−15.6351	−1.51150	−0.755750	+	0.654860i	$0.772728\pi$
$108$	9.16795	0.882187
$109$	2.38803	0.228732	0.114366	−	0.993439i	$-0.463516\pi$
$109$	2.38803	0.228732	0.114366	+	0.993439i	$0.463516\pi$
$110$	0.545883	0.0520479
$111$	−3.16311	−0.300229
$112$	10.6567	1.00696
$113$	19.0073	1.78805	0.894027	−	0.448013i	$-0.147868\pi$
$113$	19.0073	1.78805	0.894027	+	0.448013i	$0.147868\pi$
$114$	−6.15881	−0.576825
$115$	0.0313816	0.00292635
$116$	1.56412	0.145225
$117$	−2.59064	−0.239505
$118$	−3.03058	−0.278988
$119$	22.6083	2.07250
$120$	0.0898213	0.00819952
$121$	−6.20640	−0.564218
$122$	−4.66224	−0.422100
$123$	−5.59820	−0.504773
$124$	9.32786	0.837667
$125$	−1.16560	−0.104254
$126$	−23.0652	−2.05481
$127$	8.19019	0.726762	0.363381	−	0.931641i	$-0.381622\pi$
$127$	8.19019	0.726762	0.363381	+	0.931641i	$0.381622\pi$
$128$	9.24095	0.816792
$129$	−3.81593	−0.335974
$130$	−0.249327	−0.0218674
$131$	−2.51100	−0.219387	−0.109693	−	0.993965i	$-0.534987\pi$
$131$	−2.51100	−0.219387	−0.109693	+	0.993965i	$0.534987\pi$
$132$	3.59039	0.312503
$133$	18.7819	1.62860
$134$	−22.6252	−1.95452
$135$	0.417497	0.0359324
$136$	6.52432	0.559456
$137$	−17.8505	−1.52507	−0.762537	−	0.646944i	$-0.776047\pi$
$137$	−17.8505	−1.52507	−0.762537	+	0.646944i	$0.776047\pi$
$138$	0.367463	0.0312805
$139$	5.60718	0.475595	0.237798	−	0.971315i	$-0.423575\pi$
$139$	5.60718	0.475595	0.237798	+	0.971315i	$0.423575\pi$
$140$	−1.24687	−0.105380
$141$	6.47096	0.544953
$142$	−10.0826	−0.846113
$143$	−2.18943	−0.183089
$144$	6.62382	0.551985
$145$	0.0712282	0.00591518
$146$	−1.80088	−0.149042
$147$	−6.63592	−0.547322
$148$	12.6714	1.04158
$149$	3.99332	0.327146	0.163573	−	0.986531i	$-0.447698\pi$
$149$	3.99332	0.327146	0.163573	+	0.986531i	$0.447698\pi$
$150$	−6.81497	−0.556440
$151$	−15.5900	−1.26870	−0.634349	−	0.773046i	$-0.718732\pi$
$151$	−15.5900	−1.26870	−0.634349	+	0.773046i	$0.718732\pi$
$152$	5.42008	0.439627
$153$	14.0525	1.13608
$154$	−19.4931	−1.57080
$155$	0.424779	0.0341190
$156$	−1.63987	−0.131295
$157$	−7.17438	−0.572578	−0.286289	−	0.958143i	$-0.592422\pi$
$157$	−7.17438	−0.572578	−0.286289	+	0.958143i	$0.592422\pi$
$158$	4.16909	0.331675
$159$	−6.11880	−0.485253
$160$	0.918260	0.0725948
$161$	−1.12061	−0.0883167
$162$	−11.7132	−0.920276
$163$	−16.2187	−1.27035	−0.635173	−	0.772370i	$-0.719071\pi$
$163$	−16.2187	−1.27035	−0.635173	+	0.772370i	$0.719071\pi$
$164$	22.4263	1.75120
$165$	0.163502	0.0127286
$166$	23.8736	1.85295
$167$	21.4210	1.65761	0.828804	−	0.559538i	$-0.189022\pi$
$167$	21.4210	1.65761	0.828804	+	0.559538i	$0.189022\pi$
$168$	−3.20745	−0.247460
$169$	1.00000	0.0769231
$170$	1.35243	0.103727
$171$	11.6742	0.892745
$172$	15.2865	1.16559
$173$	−3.76276	−0.286077	−0.143039	−	0.989717i	$-0.545687\pi$
$173$	−3.76276	−0.286077	−0.143039	+	0.989717i	$0.545687\pi$
$174$	0.834047	0.0632290
$175$	20.7829	1.57104
$176$	5.59798	0.421964
$177$	−0.907712	−0.0682278
$178$	−6.89388	−0.516718
$179$	−0.867106	−0.0648105	−0.0324053	−	0.999475i	$-0.510317\pi$
$179$	−0.867106	−0.0648105	−0.0324053	+	0.999475i	$0.510317\pi$
$180$	−0.775011	−0.0577659
$181$	5.36722	0.398942	0.199471	−	0.979904i	$-0.436078\pi$
$181$	5.36722	0.398942	0.199471	+	0.979904i	$0.436078\pi$
$182$	8.90327	0.659955
$183$	−1.39642	−0.103227
$184$	−0.323387	−0.0238404
$185$	0.577038	0.0424247
$186$	4.97395	0.364708
$187$	11.8762	0.868475
$188$	−25.9226	−1.89060
$189$	−14.9085	−1.08443
$190$	1.12353	0.0815098
$191$	−22.7940	−1.64932	−0.824659	−	0.565630i	$-0.808633\pi$
$191$	−22.7940	−1.64932	−0.824659	+	0.565630i	$0.808633\pi$
$192$	7.48061	0.539866
$193$	−9.98339	−0.718620	−0.359310	−	0.933218i	$-0.616988\pi$
$193$	−9.98339	−0.718620	−0.359310	+	0.933218i	$0.616988\pi$
$194$	−16.1851	−1.16202
$195$	−0.0746777	−0.00534778
$196$	26.5834	1.89881
$197$	−8.58741	−0.611828	−0.305914	−	0.952059i	$-0.598962\pi$
$197$	−8.58741	−0.611828	−0.305914	+	0.952059i	$0.598962\pi$
$198$	−12.1162	−0.861062
$199$	−21.1283	−1.49775	−0.748874	−	0.662713i	$-0.769405\pi$
$199$	−21.1283	−1.49775	−0.748874	+	0.662713i	$0.769405\pi$
$200$	5.99754	0.424090
$201$	−6.77664	−0.477987
$202$	−21.0328	−1.47986
$203$	−2.54351	−0.178519
$204$	8.89525	0.622792
$205$	1.02126	0.0713282
$206$	−14.5895	−1.01650
$207$	−0.696533	−0.0484124
$208$	−2.55682	−0.177284
$209$	9.86617	0.682457
$210$	−0.664876	−0.0458808
$211$	2.90551	0.200023	0.100012	−	0.994986i	$-0.468112\pi$
$211$	2.90551	0.200023	0.100012	+	0.994986i	$0.468112\pi$
$212$	24.5118	1.68348
$213$	−3.01992	−0.206921
$214$	33.3986	2.28308
$215$	0.696129	0.0474756
$216$	−4.30230	−0.292734
$217$	−15.1685	−1.02971
$218$	−5.10116	−0.345494
$219$	−0.539396	−0.0364490
$220$	−0.654985	−0.0441591
$221$	−5.42435	−0.364881
$222$	6.75683	0.453489
$223$	−8.13499	−0.544759	−0.272380	−	0.962190i	$-0.587811\pi$
$223$	−8.13499	−0.544759	−0.272380	+	0.962190i	$0.587811\pi$
$224$	−32.7904	−2.19090
$225$	12.9179	0.861195
$226$	−40.6021	−2.70081
$227$	25.9451	1.72204	0.861020	−	0.508571i	$-0.169826\pi$
$227$	25.9451	1.72204	0.861020	+	0.508571i	$0.169826\pi$
$228$	7.38972	0.489396
$229$	4.12978	0.272903	0.136452	−	0.990647i	$-0.456430\pi$
$229$	4.12978	0.272903	0.136452	+	0.990647i	$0.456430\pi$
$230$	−0.0670352	−0.00442017
$231$	−5.83852	−0.384147
$232$	−0.734006	−0.0481899
$233$	19.1228	1.25278	0.626389	−	0.779510i	$-0.284532\pi$
$233$	19.1228	1.25278	0.626389	+	0.779510i	$0.284532\pi$
$234$	5.53396	0.361766
$235$	−1.18048	−0.0770060
$236$	3.63628	0.236702
$237$	1.24872	0.0811128
$238$	−48.2944	−3.13046
$239$	4.68204	0.302856	0.151428	−	0.988468i	$-0.451613\pi$
$239$	4.68204	0.302856	0.151428	+	0.988468i	$0.451613\pi$
$240$	0.190938	0.0123250
$241$	−8.01668	−0.516400	−0.258200	−	0.966092i	$-0.583129\pi$
$241$	−8.01668	−0.516400	−0.258200	+	0.966092i	$0.583129\pi$
$242$	13.2577	0.852237
$243$	−14.2392	−0.913442
$244$	5.59405	0.358123
$245$	1.21057	0.0773407
$246$	11.9585	0.762447
$247$	−4.50627	−0.286727
$248$	−4.37734	−0.277961
$249$	7.15055	0.453148
$250$	2.48987	0.157473
$251$	−5.42543	−0.342450	−0.171225	−	0.985232i	$-0.554772\pi$
$251$	−5.42543	−0.342450	−0.171225	+	0.985232i	$0.554772\pi$
$252$	27.6751	1.74337
$253$	−0.588661	−0.0370088
$254$	−17.4953	−1.09776
$255$	0.405078	0.0253670
$256$	3.64396	0.227747
$257$	−26.2750	−1.63899	−0.819494	−	0.573088i	$-0.805745\pi$
$257$	−26.2750	−1.63899	−0.819494	+	0.573088i	$0.805745\pi$
$258$	8.15133	0.507479
$259$	−20.6056	−1.28037
$260$	0.299158	0.0185530
$261$	−1.58095	−0.0978586
$262$	5.36383	0.331378
$263$	4.34782	0.268098	0.134049	−	0.990975i	$-0.457202\pi$
$263$	4.34782	0.268098	0.134049	+	0.990975i	$0.457202\pi$
$264$	−1.68488	−0.103697
$265$	1.11624	0.0685699
$266$	−40.1206	−2.45995
$267$	−2.06484	−0.126366
$268$	27.1471	1.65827
$269$	−27.7793	−1.69373	−0.846867	−	0.531804i	$-0.821514\pi$
$269$	−27.7793	−1.69373	−0.846867	+	0.531804i	$0.821514\pi$
$270$	−0.891829	−0.0542750
$271$	2.34602	0.142511	0.0712553	−	0.997458i	$-0.477300\pi$
$271$	2.34602	0.142511	0.0712553	+	0.997458i	$0.477300\pi$
$272$	13.8691	0.840937
$273$	2.66669	0.161395
$274$	38.1311	2.30359
$275$	10.9173	0.658339
$276$	−0.440905	−0.0265393
$277$	−5.79566	−0.348227	−0.174114	−	0.984726i	$-0.555706\pi$
$277$	−5.79566	−0.348227	−0.174114	+	0.984726i	$0.555706\pi$
$278$	−11.9777	−0.718374
$279$	−9.42822	−0.564453
$280$	0.585127	0.0349680
$281$	12.6136	0.752462	0.376231	−	0.926526i	$-0.377220\pi$
$281$	12.6136	0.752462	0.376231	+	0.926526i	$0.377220\pi$
$282$	−13.8228	−0.823138
$283$	5.76424	0.342648	0.171324	−	0.985215i	$-0.445195\pi$
$283$	5.76424	0.342648	0.171324	+	0.985215i	$0.445195\pi$
$284$	12.0977	0.717869
$285$	0.336518	0.0199336
$286$	4.67691	0.276552
$287$	−36.4686	−2.15267
$288$	−20.3813	−1.20098
$289$	12.4235	0.730796
$290$	−0.152153	−0.00893473
$291$	−4.84773	−0.284179
$292$	2.16081	0.126452
$293$	17.2908	1.01014	0.505071	−	0.863078i	$-0.331466\pi$
$293$	17.2908	1.01014	0.505071	+	0.863078i	$0.331466\pi$
$294$	14.1752	0.826715
$295$	0.165592	0.00964111
$296$	−5.94637	−0.345626
$297$	−7.83147	−0.454428
$298$	−8.53027	−0.494145
$299$	0.268865	0.0155489
$300$	8.17703	0.472101
$301$	−24.8583	−1.43281
$302$	33.3024	1.91634
$303$	−6.29969	−0.361908
$304$	11.5217	0.660818
$305$	0.254746	0.0145867
$306$	−30.0181	−1.71602
$307$	16.1681	0.922761	0.461380	−	0.887202i	$-0.347354\pi$
$307$	16.1681	0.922761	0.461380	+	0.887202i	$0.347354\pi$
$308$	23.3890	1.33271
$309$	−4.36981	−0.248590
$310$	−0.907384	−0.0515359
$311$	−20.3183	−1.15215	−0.576073	−	0.817398i	$-0.695416\pi$
$311$	−20.3183	−1.15215	−0.576073	+	0.817398i	$0.695416\pi$
$312$	0.769553	0.0435674
$313$	−16.7036	−0.944141	−0.472070	−	0.881561i	$-0.656493\pi$
$313$	−16.7036	−0.944141	−0.472070	+	0.881561i	$0.656493\pi$
$314$	15.3254	0.864865
$315$	1.26029	0.0710091
$316$	−5.00233	−0.281403
$317$	18.4561	1.03660	0.518298	−	0.855200i	$-0.326566\pi$
$317$	18.4561	1.03660	0.518298	+	0.855200i	$0.326566\pi$
$318$	13.0706	0.732962
$319$	−1.33611	−0.0748078
$320$	−1.36467	−0.0762872
$321$	10.0035	0.558339
$322$	2.39378	0.133400
$323$	24.4436	1.36008
$324$	14.0542	0.780791
$325$	−4.98638	−0.276594
$326$	34.6453	1.91883
$327$	−1.52789	−0.0844924
$328$	−10.5241	−0.581098
$329$	42.1540	2.32403
$330$	−0.349261	−0.0192262
$331$	11.1424	0.612442	0.306221	−	0.951961i	$-0.400935\pi$
$331$	11.1424	0.612442	0.306221	+	0.951961i	$0.400935\pi$
$332$	−28.6450	−1.57210
$333$	−12.8077	−0.701858
$334$	−45.7582	−2.50378
$335$	1.23624	0.0675432
$336$	−6.81825	−0.371966
$337$	−10.3952	−0.566263	−0.283131	−	0.959081i	$-0.591373\pi$
$337$	−10.3952	−0.566263	−0.283131	+	0.959081i	$0.591373\pi$
$338$	−2.13613	−0.116190
$339$	−12.1610	−0.660497
$340$	−1.62274	−0.0880052
$341$	−7.96807	−0.431495
$342$	−24.9375	−1.34847
$343$	−14.0531	−0.758797
$344$	−7.17360	−0.386775
$345$	−0.0200782	−0.00108098
$346$	8.03776	0.432113
$347$	31.7670	1.70534	0.852670	−	0.522450i	$-0.174982\pi$
$347$	31.7670	1.70534	0.852670	+	0.522450i	$0.174982\pi$
$348$	−1.00074	−0.0536454
$349$	2.04418	0.109422	0.0547111	−	0.998502i	$-0.482576\pi$
$349$	2.04418	0.109422	0.0547111	+	0.998502i	$0.482576\pi$
$350$	−44.3951	−2.37302
$351$	3.57695	0.190923
$352$	−17.2249	−0.918089
$353$	3.96675	0.211129	0.105564	−	0.994412i	$-0.466335\pi$
$353$	3.96675	0.211129	0.105564	+	0.994412i	$0.466335\pi$
$354$	1.93899	0.103056
$355$	0.550915	0.0292396
$356$	8.27170	0.438399
$357$	−14.4650	−0.765571
$358$	1.85225	0.0978947
$359$	−2.48877	−0.131352	−0.0656761	−	0.997841i	$-0.520920\pi$
$359$	−2.48877	−0.131352	−0.0656761	+	0.997841i	$0.520920\pi$
$360$	0.363694	0.0191684
$361$	1.30651	0.0687638
$362$	−11.4651	−0.602592
$363$	3.97091	0.208419
$364$	−10.6827	−0.559926
$365$	0.0984006	0.00515052
$366$	2.98295	0.155921
$367$	−18.0200	−0.940634	−0.470317	−	0.882498i	$-0.655860\pi$
$367$	−18.0200	−0.940634	−0.470317	+	0.882498i	$0.655860\pi$
$368$	−0.687440	−0.0358353
$369$	−22.6676	−1.18003
$370$	−1.23263	−0.0640814
$371$	−39.8600	−2.06943
$372$	−5.96805	−0.309429
$373$	21.7523	1.12629	0.563146	−	0.826357i	$-0.309591\pi$
$373$	21.7523	1.12629	0.563146	+	0.826357i	$0.309591\pi$
$374$	−25.3692	−1.31181
$375$	0.745760	0.0385109
$376$	12.1648	0.627353
$377$	0.610255	0.0314297
$378$	31.8465	1.63801
$379$	17.8322	0.915977	0.457989	−	0.888958i	$-0.348570\pi$
$379$	17.8322	0.915977	0.457989	+	0.888958i	$0.348570\pi$
$380$	−1.34809	−0.0691554
$381$	−5.24016	−0.268462
$382$	48.6911	2.49125
$383$	2.96331	0.151418	0.0757091	−	0.997130i	$-0.475878\pi$
$383$	2.96331	0.151418	0.0757091	+	0.997130i	$0.475878\pi$
$384$	−5.91245	−0.301718
$385$	1.06511	0.0542828
$386$	21.3259	1.08546
$387$	−15.4510	−0.785419
$388$	19.4199	0.985898
$389$	−17.3684	−0.880611	−0.440305	−	0.897848i	$-0.645130\pi$
$389$	−17.3684	−0.880611	−0.440305	+	0.897848i	$0.645130\pi$
$390$	0.159522	0.00807769
$391$	−1.45842	−0.0737553
$392$	−12.4749	−0.630080
$393$	1.60656	0.0810403
$394$	18.3439	0.924150
$395$	−0.227800	−0.0114619
$396$	14.5378	0.730552
$397$	−10.9000	−0.547058	−0.273529	−	0.961864i	$-0.588191\pi$
$397$	−10.9000	−0.547058	−0.273529	+	0.961864i	$0.588191\pi$
$398$	45.1329	2.26231
$399$	−12.0168	−0.601594
$400$	12.7493	0.637464
$401$	3.41055	0.170315	0.0851574	−	0.996368i	$-0.472861\pi$
$401$	3.41055	0.170315	0.0851574	+	0.996368i	$0.472861\pi$
$402$	14.4758	0.721988
$403$	3.63934	0.181288
$404$	25.2364	1.25556
$405$	0.640012	0.0318024
$406$	5.43327	0.269649
$407$	−10.8242	−0.536535
$408$	−4.17432	−0.206660
$409$	9.93654	0.491330	0.245665	−	0.969355i	$-0.420994\pi$
$409$	9.93654	0.491330	0.245665	+	0.969355i	$0.420994\pi$
$410$	−2.18156	−0.107739
$411$	11.4209	0.563354
$412$	17.5054	0.862428
$413$	−5.91315	−0.290967
$414$	1.48789	0.0731257
$415$	−1.30446	−0.0640332
$416$	7.86729	0.385725
$417$	−3.58753	−0.175682
$418$	−21.0755	−1.03083
$419$	31.7402	1.55061	0.775306	−	0.631585i	$-0.217595\pi$
$419$	31.7402	1.55061	0.775306	+	0.631585i	$0.217595\pi$
$420$	0.797760	0.0389267
$421$	8.80466	0.429113	0.214556	−	0.976712i	$-0.431169\pi$
$421$	8.80466	0.429113	0.214556	+	0.976712i	$0.431169\pi$
$422$	−6.20655	−0.302130
$423$	26.2015	1.27396
$424$	−11.5028	−0.558626
$425$	27.0478	1.31201
$426$	6.45095	0.312549
$427$	−9.09679	−0.440224
$428$	−40.0737	−1.93704
$429$	1.40082	0.0676321
$430$	−1.48702	−0.0717107
$431$	1.28633	0.0619603	0.0309801	−	0.999520i	$-0.490137\pi$
$431$	1.28633	0.0619603	0.0309801	+	0.999520i	$0.490137\pi$
$432$	−9.14562	−0.440019
$433$	−24.1438	−1.16028	−0.580138	−	0.814518i	$-0.697001\pi$
$433$	−24.1438	−1.16028	−0.580138	+	0.814518i	$0.697001\pi$
$434$	32.4020	1.55535
$435$	−0.0455725	−0.00218503
$436$	6.12069	0.293128
$437$	−1.21158	−0.0579577
$438$	1.15222	0.0550553
$439$	−23.8971	−1.14055	−0.570274	−	0.821454i	$-0.693163\pi$
$439$	−23.8971	−1.14055	−0.570274	+	0.821454i	$0.693163\pi$
$440$	0.307369	0.0146532
$441$	−26.8694	−1.27950
$442$	11.5871	0.551143
$443$	16.5480	0.786222	0.393111	−	0.919491i	$-0.371399\pi$
$443$	16.5480	0.786222	0.393111	+	0.919491i	$0.371399\pi$
$444$	−8.10727	−0.384754
$445$	0.376683	0.0178565
$446$	17.3774	0.822845
$447$	−2.55497	−0.120846
$448$	48.7312	2.30233
$449$	−3.08214	−0.145455	−0.0727275	−	0.997352i	$-0.523170\pi$
$449$	−3.08214	−0.145455	−0.0727275	+	0.997352i	$0.523170\pi$
$450$	−27.5944	−1.30081
$451$	−19.1571	−0.902071
$452$	48.7169	2.29145
$453$	9.97465	0.468650
$454$	−55.4223	−2.60110
$455$	−0.486476	−0.0228064
$456$	−3.46782	−0.162396
$457$	34.6157	1.61925	0.809626	−	0.586946i	$-0.199670\pi$
$457$	34.6157	1.61925	0.809626	+	0.586946i	$0.199670\pi$
$458$	−8.82176	−0.412214
$459$	−19.4026	−0.905636
$460$	0.0804331	0.00375021
$461$	−0.579141	−0.0269733	−0.0134866	−	0.999909i	$-0.504293\pi$
$461$	−0.579141	−0.0269733	−0.0134866	+	0.999909i	$0.504293\pi$
$462$	12.4719	0.580244
$463$	−7.93824	−0.368921	−0.184461	−	0.982840i	$-0.559054\pi$
$463$	−7.93824	−0.368921	−0.184461	+	0.982840i	$0.559054\pi$
$464$	−1.56031	−0.0724358
$465$	−0.271777	−0.0126034
$466$	−40.8489	−1.89229
$467$	27.9849	1.29499	0.647493	−	0.762072i	$-0.275818\pi$
$467$	27.9849	1.29499	0.647493	+	0.762072i	$0.275818\pi$
$468$	−6.63999	−0.306934
$469$	−44.1454	−2.03844
$470$	2.52166	0.116316
$471$	4.59024	0.211507
$472$	−1.70642	−0.0785443
$473$	−13.0581	−0.600412
$474$	−2.66742	−0.122519
$475$	22.4700	1.03099
$476$	57.9467	2.65598
$477$	−24.7756	−1.13439
$478$	−10.0015	−0.457456
$479$	32.5816	1.48869	0.744347	−	0.667794i	$-0.232761\pi$
$479$	32.5816	1.48869	0.744347	+	0.667794i	$0.232761\pi$
$480$	−0.587511	−0.0268161
$481$	4.94383	0.225419
$482$	17.1247	0.780009
$483$	0.716979	0.0326237
$484$	−15.9074	−0.723064
$485$	0.884359	0.0401567
$486$	30.4167	1.37973
$487$	17.5645	0.795921	0.397961	−	0.917402i	$-0.369718\pi$
$487$	17.5645	0.795921	0.397961	+	0.917402i	$0.369718\pi$
$488$	−2.62515	−0.118835
$489$	10.3769	0.469259
$490$	−2.58595	−0.116821
$491$	−38.3563	−1.73100	−0.865498	−	0.500912i	$-0.832998\pi$
$491$	−38.3563	−1.73100	−0.865498	+	0.500912i	$0.832998\pi$
$492$	−14.3486	−0.646883
$493$	−3.31024	−0.149086
$494$	9.62600	0.433094
$495$	0.662032	0.0297561
$496$	−9.30514	−0.417813
$497$	−19.6728	−0.882445
$498$	−15.2745	−0.684468
$499$	−4.38411	−0.196259	−0.0981297	−	0.995174i	$-0.531286\pi$
$499$	−4.38411	−0.196259	−0.0981297	+	0.995174i	$0.531286\pi$
$500$	−2.98750	−0.133605
$501$	−13.7054	−0.612311
$502$	11.5894	0.517262
$503$	22.8439	1.01856	0.509280	−	0.860601i	$-0.329912\pi$
$503$	22.8439	1.01856	0.509280	+	0.860601i	$0.329912\pi$
$504$	−12.9872	−0.578498
$505$	1.14923	0.0511403
$506$	1.25746	0.0559008
$507$	−0.639809	−0.0284149
$508$	20.9920	0.931369
$509$	6.47904	0.287178	0.143589	−	0.989637i	$-0.454136\pi$
$509$	6.47904	0.287178	0.143589	+	0.989637i	$0.454136\pi$
$510$	−0.865300	−0.0383161
$511$	−3.51381	−0.155442
$512$	−26.2659	−1.16080
$513$	−16.1187	−0.711658
$514$	56.1268	2.47565
$515$	0.797172	0.0351276
$516$	−9.78047	−0.430561
$517$	22.1436	0.973876
$518$	44.0163	1.93397
$519$	2.40745	0.105675
$520$	−0.140388	−0.00615640
$521$	20.8086	0.911642	0.455821	−	0.890072i	$-0.349346\pi$
$521$	20.8086	0.911642	0.455821	+	0.890072i	$0.349346\pi$
$522$	3.37713	0.147813
$523$	24.7318	1.08144	0.540722	−	0.841201i	$-0.318151\pi$
$523$	24.7318	1.08144	0.540722	+	0.841201i	$0.318151\pi$
$524$	−6.43586	−0.281152
$525$	−13.2971	−0.580333
$526$	−9.28753	−0.404955
$527$	−19.7410	−0.859932
$528$	−3.58164	−0.155871
$529$	−22.9277	−0.996857
$530$	−2.38443	−0.103573
$531$	−3.67541	−0.159499
$532$	48.1392	2.08710
$533$	8.74980	0.378996
$534$	4.41077	0.190873
$535$	−1.82491	−0.0788976
$536$	−12.7395	−0.550262
$537$	0.554783	0.0239406
$538$	59.3403	2.55834
$539$	−22.7081	−0.978109
$540$	1.07007	0.0460486
$541$	27.9528	1.20178	0.600891	−	0.799331i	$-0.294812\pi$
$541$	27.9528	1.20178	0.600891	+	0.799331i	$0.294812\pi$
$542$	−5.01141	−0.215259
$543$	−3.43400	−0.147367
$544$	−42.6749	−1.82967
$545$	0.278728	0.0119394
$546$	−5.69640	−0.243783
$547$	−21.2347	−0.907929	−0.453965	−	0.891020i	$-0.649991\pi$
$547$	−21.2347	−0.907929	−0.453965	+	0.891020i	$0.649991\pi$
$548$	−45.7521	−1.95443
$549$	−5.65424	−0.241317
$550$	−23.3209	−0.994405
$551$	−2.74998	−0.117153
$552$	0.206906	0.00880650
$553$	8.13456	0.345917
$554$	12.3803	0.525988
$555$	−0.369194	−0.0156714
$556$	14.3716	0.609491
$557$	15.2969	0.648149	0.324075	−	0.946031i	$-0.394947\pi$
$557$	15.2969	0.648149	0.324075	+	0.946031i	$0.394947\pi$
$558$	20.1399	0.852592
$559$	5.96416	0.252257
$560$	1.24383	0.0525616
$561$	−7.59852	−0.320810
$562$	−26.9442	−1.13657
$563$	22.0134	0.927756	0.463878	−	0.885899i	$-0.346458\pi$
$563$	22.0134	0.927756	0.463878	+	0.885899i	$0.346458\pi$
$564$	16.5855	0.698375
$565$	2.21850	0.0933332
$566$	−12.3132	−0.517561
$567$	−22.8543	−0.959792
$568$	−5.67718	−0.238209
$569$	29.0560	1.21809	0.609045	−	0.793136i	$-0.291553\pi$
$569$	29.0560	1.21809	0.609045	+	0.793136i	$0.291553\pi$
$570$	−0.718848	−0.0301092
$571$	−8.09495	−0.338763	−0.169381	−	0.985551i	$-0.554177\pi$
$571$	−8.09495	−0.338763	−0.169381	+	0.985551i	$0.554177\pi$
$572$	−5.61165	−0.234635
$573$	14.5838	0.609249
$574$	77.9018	3.25156
$575$	−1.34066	−0.0559095
$576$	30.2896	1.26207
$577$	−0.235606	−0.00980841	−0.00490420	−	0.999988i	$-0.501561\pi$
$577$	−0.235606	−0.00980841	−0.00490420	+	0.999988i	$0.501561\pi$
$578$	−26.5383	−1.10385
$579$	6.38747	0.265454
$580$	0.182563	0.00758050
$581$	46.5811	1.93251
$582$	10.3554	0.429245
$583$	−20.9386	−0.867186
$584$	−1.01402	−0.0419603
$585$	−0.302377	−0.0125017
$586$	−36.9355	−1.52579
$587$	0.453552	0.0187201	0.00936004	−	0.999956i	$-0.497021\pi$
$587$	0.453552	0.0187201	0.00936004	+	0.999956i	$0.497021\pi$
$588$	−17.0083	−0.701411
$589$	−16.3998	−0.675744
$590$	−0.353726	−0.0145627
$591$	5.49431	0.226006
$592$	−12.6405	−0.519522
$593$	20.8015	0.854214	0.427107	−	0.904201i	$-0.359533\pi$
$593$	20.8015	0.854214	0.427107	+	0.904201i	$0.359533\pi$
$594$	16.7291	0.686402
$595$	2.63882	0.108181
$596$	10.2352	0.419248
$597$	13.5181	0.553259
$598$	−0.574332	−0.0234862
$599$	1.30736	0.0534173	0.0267086	−	0.999643i	$-0.491497\pi$
$599$	1.30736	0.0534173	0.0267086	+	0.999643i	$0.491497\pi$
$600$	−3.83728	−0.156656
$601$	−14.5430	−0.593221	−0.296610	−	0.954999i	$-0.595856\pi$
$601$	−14.5430	−0.593221	−0.296610	+	0.954999i	$0.595856\pi$
$602$	53.1005	2.16422
$603$	−27.4392	−1.11741
$604$	−39.9583	−1.62588
$605$	−0.724403	−0.0294512
$606$	13.4570	0.546652
$607$	−15.1901	−0.616546	−0.308273	−	0.951298i	$-0.599751\pi$
$607$	−15.1901	−0.616546	−0.308273	+	0.951298i	$0.599751\pi$
$608$	−35.4522	−1.43777
$609$	1.62736	0.0659439
$610$	−0.544171	−0.0220328
$611$	−10.1139	−0.409164
$612$	36.0176	1.45593
$613$	28.3113	1.14348	0.571740	−	0.820435i	$-0.306268\pi$
$613$	28.3113	1.14348	0.571740	+	0.820435i	$0.306268\pi$
$614$	−34.5372	−1.39381
$615$	−0.653415	−0.0263482
$616$	−10.9759	−0.442232
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	9.33449	0.375488
$619$	2.69966	0.108508	0.0542542	−	0.998527i	$-0.482722\pi$
$619$	2.69966	0.108508	0.0542542	+	0.998527i	$0.482722\pi$
$620$	1.08874	0.0437247
$621$	0.961716	0.0385923
$622$	43.4026	1.74029
$623$	−13.4511	−0.538905
$624$	1.63588	0.0654876
$625$	24.7958	0.991833
$626$	35.6810	1.42610
$627$	−6.31247	−0.252096
$628$	−18.3884	−0.733778
$629$	−26.8171	−1.06927
$630$	−2.69214	−0.107258
$631$	−38.1054	−1.51695	−0.758477	−	0.651700i	$-0.774056\pi$
$631$	−38.1054	−1.51695	−0.758477	+	0.651700i	$0.774056\pi$
$632$	2.34747	0.0933775
$633$	−1.85897	−0.0738875
$634$	−39.4246	−1.56575
$635$	0.955948	0.0379357
$636$	−15.6829	−0.621867
$637$	10.3717	0.410942
$638$	2.85411	0.112995
$639$	−12.2279	−0.483728
$640$	1.07859	0.0426351
$641$	−35.5314	−1.40341	−0.701703	−	0.712469i	$-0.747577\pi$
$641$	−35.5314	−1.40341	−0.701703	+	0.712469i	$0.747577\pi$
$642$	−21.3688	−0.843357
$643$	−18.8499	−0.743369	−0.371684	−	0.928359i	$-0.621220\pi$
$643$	−18.8499	−0.743369	−0.371684	+	0.928359i	$0.621220\pi$
$644$	−2.87221	−0.113181
$645$	−0.445390	−0.0175372
$646$	−52.2148	−2.05436
$647$	22.2327	0.874058	0.437029	−	0.899447i	$-0.356031\pi$
$647$	22.2327	0.874058	0.437029	+	0.899447i	$0.356031\pi$
$648$	−6.59531	−0.259088
$649$	−3.10619	−0.121929
$650$	10.6516	0.417789
$651$	9.70497	0.380368
$652$	−41.5696	−1.62799
$653$	23.6639	0.926039	0.463019	−	0.886348i	$-0.346766\pi$
$653$	23.6639	0.926039	0.463019	+	0.886348i	$0.346766\pi$
$654$	3.26377	0.127624
$655$	−0.293081	−0.0114516
$656$	−22.3717	−0.873467
$657$	−2.18406	−0.0852084
$658$	−90.0467	−3.51038
$659$	−47.8858	−1.86536	−0.932682	−	0.360699i	$-0.882538\pi$
$659$	−47.8858	−1.86536	−0.932682	+	0.360699i	$0.882538\pi$
$660$	0.419066	0.0163121
$661$	−3.56827	−0.138790	−0.0693949	−	0.997589i	$-0.522107\pi$
$661$	−3.56827	−0.138790	−0.0693949	+	0.997589i	$0.522107\pi$
$662$	−23.8017	−0.925078
$663$	3.47055	0.134785
$664$	13.4424	0.521666
$665$	2.19220	0.0850097
$666$	27.3590	1.06014
$667$	0.164076	0.00635306
$668$	54.9035	2.12428
$669$	5.20484	0.201231
$670$	−2.64078	−0.102022
$671$	−4.77857	−0.184475
$672$	20.9796	0.809305
$673$	−33.4765	−1.29042	−0.645212	−	0.764004i	$-0.723231\pi$
$673$	−33.4765	−1.29042	−0.645212	+	0.764004i	$0.723231\pi$
$674$	22.2055	0.855326
$675$	−17.8360	−0.686508
$676$	2.56307	0.0985795
$677$	−36.3932	−1.39870	−0.699351	−	0.714778i	$-0.746528\pi$
$677$	−36.3932	−1.39870	−0.699351	+	0.714778i	$0.746528\pi$
$678$	25.9776	0.997664
$679$	−31.5798	−1.21192
$680$	0.761511	0.0292026
$681$	−16.5999	−0.636111
$682$	17.0209	0.651762
$683$	−17.5353	−0.670969	−0.335484	−	0.942046i	$-0.608900\pi$
$683$	−17.5353	−0.670969	−0.335484	+	0.942046i	$0.608900\pi$
$684$	29.9216	1.14408
$685$	−2.08349	−0.0796061
$686$	30.0193	1.14614
$687$	−2.64227	−0.100809
$688$	−15.2493	−0.581374
$689$	9.56348	0.364339
$690$	0.0428898	0.00163279
$691$	−11.8126	−0.449371	−0.224686	−	0.974431i	$-0.572136\pi$
$691$	−11.8126	−0.449371	−0.224686	+	0.974431i	$0.572136\pi$
$692$	−9.64420	−0.366618
$693$	−23.6407	−0.898035
$694$	−67.8585	−2.57587
$695$	0.654463	0.0248252
$696$	0.469624	0.0178011
$697$	−47.4619	−1.79775
$698$	−4.36663	−0.165280
$699$	−12.2350	−0.462769
$700$	53.2680	2.01334
$701$	−28.9909	−1.09497	−0.547486	−	0.836815i	$-0.684415\pi$
$701$	−28.9909	−1.09497	−0.547486	+	0.836815i	$0.684415\pi$
$702$	−7.64084	−0.288385
$703$	−22.2783	−0.840241
$704$	25.5987	0.964785
$705$	0.755282	0.0284456
$706$	−8.47350	−0.318904
$707$	−41.0383	−1.54341
$708$	−2.32653	−0.0874363
$709$	−15.7816	−0.592690	−0.296345	−	0.955081i	$-0.595768\pi$
$709$	−15.7816	−0.592690	−0.296345	+	0.955081i	$0.595768\pi$
$710$	−1.17683	−0.0441656
$711$	5.05616	0.189621
$712$	−3.88171	−0.145473
$713$	0.978490	0.0366447
$714$	30.8992	1.15638
$715$	−0.255547	−0.00955693
$716$	−2.22245	−0.0830569
$717$	−2.99561	−0.111873
$718$	5.31634	0.198404
$719$	−21.0178	−0.783831	−0.391915	−	0.920001i	$-0.628187\pi$
$719$	−21.0178	−0.783831	−0.391915	+	0.920001i	$0.628187\pi$
$720$	0.773123	0.0288126
$721$	−28.4664	−1.06015
$722$	−2.79088	−0.103866
$723$	5.12915	0.190755
$724$	13.7565	0.511258
$725$	−3.04296	−0.113013
$726$	−8.48240	−0.314811
$727$	−41.2107	−1.52842	−0.764210	−	0.644967i	$-0.776871\pi$
$727$	−41.2107	−1.52842	−0.764210	+	0.644967i	$0.776871\pi$
$728$	5.01314	0.185799
$729$	−7.33976	−0.271843
$730$	−0.210197	−0.00777974
$731$	−32.3517	−1.19657
$732$	−3.57913	−0.132288
$733$	−21.0344	−0.776922	−0.388461	−	0.921465i	$-0.626993\pi$
$733$	−21.0344	−0.776922	−0.388461	+	0.921465i	$0.626993\pi$
$734$	38.4930	1.42080
$735$	−0.774536	−0.0285692
$736$	2.11524	0.0779687
$737$	−23.1897	−0.854203
$738$	48.4210	1.78240
$739$	15.6149	0.574404	0.287202	−	0.957870i	$-0.407275\pi$
$739$	15.6149	0.574404	0.287202	+	0.957870i	$0.407275\pi$
$740$	1.47899	0.0543686
$741$	2.88316	0.105915
$742$	85.1462	3.12582
$743$	42.3014	1.55189	0.775945	−	0.630801i	$-0.217274\pi$
$743$	42.3014	1.55189	0.775945	+	0.630801i	$0.217274\pi$
$744$	2.80066	0.102677
$745$	0.466096	0.0170764
$746$	−46.4659	−1.70124
$747$	28.9532	1.05934
$748$	30.4395	1.11298
$749$	65.1661	2.38112
$750$	−1.59304	−0.0581697
$751$	−7.50795	−0.273969	−0.136984	−	0.990573i	$-0.543741\pi$
$751$	−7.50795	−0.273969	−0.136984	+	0.990573i	$0.543741\pi$
$752$	25.8594	0.942995
$753$	3.47124	0.126499
$754$	−1.30359	−0.0474738
$755$	−1.81965	−0.0662238
$756$	−38.2115	−1.38974
$757$	−11.8844	−0.431947	−0.215973	−	0.976399i	$-0.569292\pi$
$757$	−11.8844	−0.431947	−0.215973	+	0.976399i	$0.569292\pi$
$758$	−38.0919	−1.38356
$759$	0.376631	0.0136708
$760$	0.632625	0.0229477
$761$	7.90540	0.286571	0.143285	−	0.989681i	$-0.454233\pi$
$761$	7.90540	0.286571	0.143285	+	0.989681i	$0.454233\pi$
$762$	11.1937	0.405504
$763$	−9.95318	−0.360329
$764$	−58.4226	−2.11366
$765$	1.64020	0.0593014
$766$	−6.33003	−0.228713
$767$	1.41872	0.0512271
$768$	−2.33144	−0.0841286
$769$	−51.4742	−1.85621	−0.928103	−	0.372324i	$-0.878561\pi$
$769$	−51.4742	−1.85621	−0.928103	+	0.372324i	$0.878561\pi$
$770$	−2.27521	−0.0819928
$771$	16.8110	0.605432
$772$	−25.5881	−0.920936
$773$	13.5595	0.487700	0.243850	−	0.969813i	$-0.421590\pi$
$773$	13.5595	0.487700	0.243850	+	0.969813i	$0.421590\pi$
$774$	33.0054	1.18636
$775$	−18.1471	−0.651863
$776$	−9.11331	−0.327149
$777$	13.1837	0.472961
$778$	37.1011	1.33014
$779$	−39.4290	−1.41269
$780$	−0.191404	−0.00685336
$781$	−10.3342	−0.369785
$782$	3.11537	0.111406
$783$	2.18285	0.0780087
$784$	−26.5186	−0.947094
$785$	−0.837385	−0.0298875
$786$	−3.43183	−0.122409
$787$	−9.35235	−0.333375	−0.166688	−	0.986010i	$-0.553307\pi$
$787$	−9.35235	−0.333375	−0.166688	+	0.986010i	$0.553307\pi$
$788$	−22.0101	−0.784078
$789$	−2.78178	−0.0990339
$790$	0.486611	0.0173128
$791$	−79.2212	−2.81678
$792$	−6.82224	−0.242418
$793$	2.18256	0.0775051
$794$	23.2840	0.826316
$795$	−0.714179	−0.0253293
$796$	−54.1533	−1.91941
$797$	14.2050	0.503167	0.251584	−	0.967836i	$-0.419049\pi$
$797$	14.2050	0.503167	0.251584	+	0.967836i	$0.419049\pi$
$798$	25.6695	0.908692
$799$	54.8612	1.94085
$800$	−39.2293	−1.38696
$801$	−8.36070	−0.295411
$802$	−7.28539	−0.257256
$803$	−1.84582	−0.0651374
$804$	−17.3690	−0.612557
$805$	−0.130797	−0.00460997
$806$	−7.77411	−0.273831
$807$	17.7735	0.625656
$808$	−11.8429	−0.416630
$809$	25.7399	0.904966	0.452483	−	0.891773i	$-0.350538\pi$
$809$	25.7399	0.904966	0.452483	+	0.891773i	$0.350538\pi$
$810$	−1.36715	−0.0480368
$811$	−21.7318	−0.763108	−0.381554	−	0.924347i	$-0.624611\pi$
$811$	−21.7318	−0.763108	−0.381554	+	0.924347i	$0.624611\pi$
$812$	−6.51918	−0.228778
$813$	−1.50101	−0.0526426
$814$	23.1219	0.810422
$815$	−1.89303	−0.0663098
$816$	−8.87358	−0.310637
$817$	−26.8761	−0.940277
$818$	−21.2258	−0.742142
$819$	10.7976	0.377300
$820$	2.61757	0.0914095
$821$	−47.0410	−1.64174	−0.820871	−	0.571114i	$-0.806511\pi$
$821$	−47.0410	−1.64174	−0.820871	+	0.571114i	$0.806511\pi$
$822$	−24.3967	−0.850931
$823$	−14.9180	−0.520007	−0.260004	−	0.965608i	$-0.583724\pi$
$823$	−14.9180	−0.520007	−0.260004	+	0.965608i	$0.583724\pi$
$824$	−8.21485	−0.286178
$825$	−6.98500	−0.243187
$826$	12.6313	0.439498
$827$	13.0808	0.454865	0.227432	−	0.973794i	$-0.426967\pi$
$827$	13.0808	0.454865	0.227432	+	0.973794i	$0.426967\pi$
$828$	−1.78526	−0.0620421
$829$	33.5136	1.16398	0.581988	−	0.813197i	$-0.302275\pi$
$829$	33.5136	1.16398	0.581988	+	0.813197i	$0.302275\pi$
$830$	2.78649	0.0967205
$831$	3.70812	0.128633
$832$	−11.6919	−0.405345
$833$	−56.2598	−1.94929
$834$	7.66344	0.265363
$835$	2.50023	0.0865242
$836$	25.2877	0.874592
$837$	13.0177	0.449958
$838$	−67.8014	−2.34216
$839$	27.8328	0.960896	0.480448	−	0.877023i	$-0.340474\pi$
$839$	27.8328	0.960896	0.480448	+	0.877023i	$0.340474\pi$
$840$	−0.374370	−0.0129170
$841$	−28.6276	−0.987158
$842$	−18.8079	−0.648164
$843$	−8.07027	−0.277955
$844$	7.44701	0.256337
$845$	0.116719	0.00401525
$846$	−55.9698	−1.92428
$847$	25.8679	0.888831
$848$	−24.4521	−0.839689
$849$	−3.68801	−0.126572
$850$	−57.7778	−1.98176
$851$	1.32922	0.0455652
$852$	−7.74025	−0.265177
$853$	43.8400	1.50105	0.750527	−	0.660840i	$-0.229800\pi$
$853$	43.8400	1.50105	0.750527	+	0.660840i	$0.229800\pi$
$854$	19.4320	0.664948
$855$	1.36259	0.0465997
$856$	18.8056	0.642764
$857$	3.01314	0.102927	0.0514634	−	0.998675i	$-0.483611\pi$
$857$	3.01314	0.102927	0.0514634	+	0.998675i	$0.483611\pi$
$858$	−2.99233	−0.102157
$859$	34.2581	1.16887	0.584435	−	0.811441i	$-0.301316\pi$
$859$	34.2581	1.16887	0.584435	+	0.811441i	$0.301316\pi$
$860$	1.78422	0.0608416
$861$	23.3330	0.795185
$862$	−2.74777	−0.0935894
$863$	−34.0234	−1.15817	−0.579085	−	0.815267i	$-0.696590\pi$
$863$	−34.0234	−1.15817	−0.579085	+	0.815267i	$0.696590\pi$
$864$	28.1409	0.957372
$865$	−0.439184	−0.0149327
$866$	51.5743	1.75257
$867$	−7.94869	−0.269952
$868$	−38.8780	−1.31960
$869$	4.27311	0.144955
$870$	0.0973489	0.00330044
$871$	10.5917	0.358884
$872$	−2.87229	−0.0972681
$873$	−19.6289	−0.664337
$874$	2.58810	0.0875436
$875$	4.85814	0.164235
$876$	−1.38251	−0.0467106
$877$	49.5190	1.67214	0.836069	−	0.548625i	$-0.184848\pi$
$877$	49.5190	1.67214	0.836069	+	0.548625i	$0.184848\pi$
$878$	51.0475	1.72277
$879$	−11.0628	−0.373140
$880$	0.653389	0.0220258
$881$	16.8787	0.568659	0.284330	−	0.958727i	$-0.408229\pi$
$881$	16.8787	0.568659	0.284330	+	0.958727i	$0.408229\pi$
$882$	57.3967	1.93265
$883$	−3.91223	−0.131657	−0.0658284	−	0.997831i	$-0.520969\pi$
$883$	−3.91223	−0.131657	−0.0658284	+	0.997831i	$0.520969\pi$
$884$	−13.9030	−0.467607
$885$	−0.105947	−0.00356137
$886$	−35.3488	−1.18757
$887$	−23.6495	−0.794073	−0.397037	−	0.917803i	$-0.629961\pi$
$887$	−23.6495	−0.794073	−0.397037	+	0.917803i	$0.629961\pi$
$888$	3.80454	0.127672
$889$	−34.1362	−1.14489
$890$	−0.804644	−0.0269717
$891$	−12.0054	−0.402198
$892$	−20.8505	−0.698127
$893$	45.5759	1.52514
$894$	5.45775	0.182534
$895$	−0.101207	−0.00338299
$896$	−38.5157	−1.28672
$897$	−0.172022	−0.00574366
$898$	6.58385	0.219706
$899$	2.22092	0.0740720
$900$	33.1095	1.10365
$901$	−51.8756	−1.72823
$902$	40.9220	1.36255
$903$	15.9045	0.529270
$904$	−22.8617	−0.760368
$905$	0.626455	0.0208241
$906$	−21.3072	−0.707884
$907$	11.2345	0.373034	0.186517	−	0.982452i	$-0.440280\pi$
$907$	11.2345	0.373034	0.186517	+	0.982452i	$0.440280\pi$
$908$	66.4991	2.20685
$909$	−25.5080	−0.846046
$910$	1.03918	0.0344484
$911$	−52.5667	−1.74161	−0.870806	−	0.491627i	$-0.836402\pi$
$911$	−52.5667	−1.74161	−0.870806	+	0.491627i	$0.836402\pi$
$912$	−7.37172	−0.244102
$913$	24.4692	0.809812
$914$	−73.9437	−2.44584
$915$	−0.162989	−0.00538824
$916$	10.5849	0.349735
$917$	10.4657	0.345607
$918$	41.4465	1.36794
$919$	−55.0573	−1.81617	−0.908086	−	0.418784i	$-0.862457\pi$
$919$	−55.0573	−1.81617	−0.908086	+	0.418784i	$0.862457\pi$
$920$	−0.0377453	−0.00124443
$921$	−10.3445	−0.340863
$922$	1.23712	0.0407425
$923$	4.72003	0.155362
$924$	−14.9645	−0.492297
$925$	−24.6518	−0.810547
$926$	16.9571	0.557246
$927$	−17.6937	−0.581138
$928$	4.80105	0.157602
$929$	31.5090	1.03378	0.516888	−	0.856053i	$-0.327090\pi$
$929$	31.5090	1.03378	0.516888	+	0.856053i	$0.327090\pi$
$930$	0.580553	0.0190371
$931$	−46.7378	−1.53177
$932$	49.0131	1.60548
$933$	12.9999	0.425596
$934$	−59.7794	−1.95604
$935$	1.38618	0.0453329
$936$	3.11599	0.101849
$937$	3.93637	0.128595	0.0642977	−	0.997931i	$-0.479519\pi$
$937$	3.93637	0.128595	0.0642977	+	0.997931i	$0.479519\pi$
$938$	94.3004	3.07902
$939$	10.6871	0.348760
$940$	−3.02565	−0.0986857
$941$	−6.99845	−0.228143	−0.114071	−	0.993473i	$-0.536389\pi$
$941$	−6.99845	−0.228143	−0.114071	+	0.993473i	$0.536389\pi$
$942$	−9.80536	−0.319476
$943$	2.35251	0.0766084
$944$	−3.62742	−0.118063
$945$	−1.74010	−0.0566055
$946$	27.8939	0.906908
$947$	29.8232	0.969122	0.484561	−	0.874757i	$-0.338979\pi$
$947$	29.8232	0.969122	0.484561	+	0.874757i	$0.338979\pi$
$948$	3.20054	0.103949
$949$	0.843058	0.0273668
$950$	−47.9989	−1.55729
$951$	−11.8084	−0.382913
$952$	−27.1930	−0.881330
$953$	50.5632	1.63790	0.818951	−	0.573864i	$-0.194556\pi$
$953$	50.5632	1.63790	0.818951	+	0.573864i	$0.194556\pi$
$954$	52.9239	1.71347
$955$	−2.66049	−0.0860915
$956$	12.0004	0.388120
$957$	0.854856	0.0276336
$958$	−69.5987	−2.24863
$959$	74.3999	2.40250
$960$	0.873127	0.0281800
$961$	−17.7552	−0.572749
$962$	−10.5607	−0.340490
$963$	40.5049	1.30525
$964$	−20.5473	−0.661783
$965$	−1.16525	−0.0375107
$966$	−1.53156	−0.0492772
$967$	−60.2452	−1.93735	−0.968677	−	0.248324i	$-0.920120\pi$
$967$	−60.2452	−1.93735	−0.968677	+	0.248324i	$0.920120\pi$
$968$	7.46497	0.239933
$969$	−15.6392	−0.502405
$970$	−1.88911	−0.0606556
$971$	3.94780	0.126691	0.0633455	−	0.997992i	$-0.479823\pi$
$971$	3.94780	0.126691	0.0633455	+	0.997992i	$0.479823\pi$
$972$	−36.4959	−1.17061
$973$	−23.3704	−0.749221
$974$	−37.5200	−1.20222
$975$	3.19033	0.102172
$976$	−5.58043	−0.178625
$977$	−48.1318	−1.53987	−0.769936	−	0.638122i	$-0.779712\pi$
$977$	−48.1318	−1.53987	−0.769936	+	0.638122i	$0.779712\pi$
$978$	−22.1664	−0.708803
$979$	−7.06588	−0.225826
$980$	3.10278	0.0991147
$981$	−6.18655	−0.197521
$982$	81.9342	2.61463
$983$	31.6163	1.00840	0.504202	−	0.863586i	$-0.331787\pi$
$983$	31.6163	1.00840	0.504202	+	0.863586i	$0.331787\pi$
$984$	6.73343	0.214654
$985$	−1.00231	−0.0319363
$986$	7.07111	0.225190
$987$	−26.9706	−0.858482
$988$	−11.5499	−0.367451
$989$	1.60355	0.0509900
$990$	−1.41419	−0.0449459
$991$	−15.1824	−0.482285	−0.241142	−	0.970490i	$-0.577522\pi$
$991$	−15.1824	−0.482285	−0.241142	+	0.970490i	$0.577522\pi$
$992$	28.6317	0.909057
$993$	−7.12901	−0.226232
$994$	42.0237	1.33291
$995$	−2.46607	−0.0781797
$996$	18.3273	0.580724
$997$	−32.3155	−1.02344	−0.511721	−	0.859152i	$-0.670992\pi$
$997$	−32.3155	−1.02344	−0.511721	+	0.859152i	$0.670992\pi$
$998$	9.36503	0.296445
$999$	17.6838	0.559492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.19	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.19	✓	134	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13613 q^{2} -0.639809 q^{3} +2.56307 q^{4} +0.116719 q^{5} +1.36672 q^{6} -4.16794 q^{7} -1.20279 q^{8} -2.59064 q^{9} +O(q^{10})\)	\(q-2.13613 q^{2} -0.639809 q^{3} +2.56307 q^{4} +0.116719 q^{5} +1.36672 q^{6} -4.16794 q^{7} -1.20279 q^{8} -2.59064 q^{9} -0.249327 q^{10} -2.18943 q^{11} -1.63987 q^{12} +1.00000 q^{13} +8.90327 q^{14} -0.0746777 q^{15} -2.55682 q^{16} -5.42435 q^{17} +5.53396 q^{18} -4.50627 q^{19} +0.299158 q^{20} +2.66669 q^{21} +4.67691 q^{22} +0.268865 q^{23} +0.769553 q^{24} -4.98638 q^{25} -2.13613 q^{26} +3.57695 q^{27} -10.6827 q^{28} +0.610255 q^{29} +0.159522 q^{30} +3.63934 q^{31} +7.86729 q^{32} +1.40082 q^{33} +11.5871 q^{34} -0.486476 q^{35} -6.63999 q^{36} +4.94383 q^{37} +9.62600 q^{38} -0.639809 q^{39} -0.140388 q^{40} +8.74980 q^{41} -5.69640 q^{42} +5.96416 q^{43} -5.61165 q^{44} -0.302377 q^{45} -0.574332 q^{46} -10.1139 q^{47} +1.63588 q^{48} +10.3717 q^{49} +10.6516 q^{50} +3.47055 q^{51} +2.56307 q^{52} +9.56348 q^{53} -7.64084 q^{54} -0.255547 q^{55} +5.01314 q^{56} +2.88316 q^{57} -1.30359 q^{58} +1.41872 q^{59} -0.191404 q^{60} +2.18256 q^{61} -7.77411 q^{62} +10.7976 q^{63} -11.6919 q^{64} +0.116719 q^{65} -2.99233 q^{66} +10.5917 q^{67} -13.9030 q^{68} -0.172022 q^{69} +1.03918 q^{70} +4.72003 q^{71} +3.11599 q^{72} +0.843058 q^{73} -10.5607 q^{74} +3.19033 q^{75} -11.5499 q^{76} +9.12541 q^{77} +1.36672 q^{78} -1.95170 q^{79} -0.298429 q^{80} +5.48337 q^{81} -18.6907 q^{82} -11.1761 q^{83} +6.83490 q^{84} -0.633123 q^{85} -12.7402 q^{86} -0.390447 q^{87} +2.63341 q^{88} +3.22727 q^{89} +0.645917 q^{90} -4.16794 q^{91} +0.689119 q^{92} -2.32848 q^{93} +21.6046 q^{94} -0.525967 q^{95} -5.03356 q^{96} +7.57684 q^{97} -22.1554 q^{98} +5.67203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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